Engineering order--from--disorder

One of the most intriguing features of frustrated magnetism is the prevalence of {\it order--from--disorder} effects, where fluctuations conspire to select a unique state from a disordered manifold of degenerate classical ground states. Quite generally, order--from--disorder effects favour collinear spin configurations, and therefore lead to magnetization plateaux in many two--dimensional frustrated spin systems. Much less is known about order from disorder in three dimensions. Here we use classical Monte Carlo and low--T expansion techniques to show how thermal fluctuations stabilize a half--magnetization plateau in a Heisenberg model on the highly frustrated, three--dimensional Pyrochlore lattice if --- and only if --- they are given a ``helping hand'' by additional longer--ranged interactions. Our results provide the first example of fluctuation--driven magnetization plateau which can be tuned at will between different ordered states.